[evlatests] weights & images, SysPower vs. REWAY

[Vivek Dhawan]

A test was done to verify that the switched power scheme worked and the
resulting calibration was reasonable. As reported previously, it is.

This extension compares the weights from REWAY, as suggested by Frazer.

In summary,

1. The weights from TYAPL and REWAY are affected by different errors, but
    agree quite well, see plot #1,top. The expected weight for this data
    is 39 Jy^-2 (rms 0.16 Jy in 1sec, 2MHz, 1 baseline). Plot#1 bottom is
    explained later.

2. With TYAPL the flux scale is good to 5-10%, biased to the high side.
    The cause might be related to how bandpass normalization is done.
    Wider testing is encouraged, sysPower is now standard with all data.

3. The use of weights from TYAPL does not mess up the detection of a weak
    source. Therefore, observation of a flux calibrator may be relaxed, e.g.,
    for transients or other short dynamic scheduling blocks. The limitations
    need to be further examined, especially for high frequency observing.

    Plot 2 shows an image made with TYAPL calibration (recipe A below). It
    is near-identical to images made by the standard route (recipe B) and
    an alternative C below.

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Observation: C band, OSRO 4832 & 4960 MHz, 3C147 + 10 scans of 1min on each
       of J0217+7349 and a blank field 1deg away.

Pro & con:  TYAPL makes weights independent of source strength (unless they
       are strong enough to raise Tsys). But its weights are tied to Tcal and
       subject to measurement error or change after lab calibration. Only one
       program, TYAPL, with no options, is run before examining the weights
       and calibration. The weights represent the expected rms, given the
       switched power calibration.

       REWAY requires calibrated data - a flux calibrator to put the rms in
       physical units; and phase calibration so that the rms is dominated by
       noise and not troposphere. Strong sources get lower weight, as their
       rms is dominated by calibration errors, delay cogging, etc. Even on a
       blank field, the weight can be examined only after several processing
       steps - your mileage varies with the options used. However, weights
       reflect the true rms in the data, regardless of origin.

The (AIPS) processing followed 3 paths A, B, C.

      BDF2AIPS, FRING, BPASS on 3C147, normalize A&P using chan 5-60. After
      this the path forks. (The BP norm may cause the small bias, since the
      switched power saw the whole subband, but I normalize on the center
      of the subband. The offset is corrected by CALIB in the usual scheme,
      path B, but not in path A. Path C attempts to correct it but fails.)

Path A: TYAPL, IMAGR.

Path B: standard calibration: SETJY, CALIB on 3C147, REWAY, IMAGR.

         The weights from A and B are compared in plot#1, top.

Path C. This is what one might do if there was no flux calibrator observed.

      Assuming the flux scale is globally correct, run CALIB on the phase
      cal as follows: Do not calibrate weights; Normalize the gains using the
      global median gain over all antennas/IFs/Pol. Then run REWAY to make
      new weights, and go to IMAGR.

      This lowered the weights, plot #1, bottom panel; not sure why - maybe
      I need to use a shorter solution to follow phase errors. But the
      weights were highly correlated with the first run of REWAY.

      The image looked the same in A, B, C.

      A weak source in the 'blank' field came out 1.3mJy in B (rms 36uJy)
      and 1.4 mJy (rms 40 uJy) for both A and C. Expected rms for robust
      weighting was 33uJy.
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